I reviewed the last five races (didn't record the anthem in 2020).
2015: A-10s, 30 seconds late
2016: F/A-18 quartet, on time
2017: B-52, 37 seconds early
2018: B-2, late (still coming when network went to commercial break)
2019: A-10, F-16, P-51, P-40, 25 seconds early
In the lower left corner the Indianapolis area is depicted at magnified scale. The concentric magenta rings around the main airport (IND) indicate the Class C airspace boundaries. Within the inner ring, Class C airspace extends from the surface to 4800 feet MSL. Between the inner and outer rings Is the "shelf" which extends from 2100 to 4800 MSL. The terrain around IND is about 800 feet above sea level, so you can fly as high as 2100 - 800 = 1300 feet AGL under the shelf and still stay out of the Class C.
The Speedway is northeast of IND, 5 miles away, right on the inner Class C ring and almost directly in line with the two main runways. The magenta diamond indicates a sporting event TFR may apply at that point. On race day the flyover after the national anthem seems to go directly over the main straight, in the same direction the cars run (south). Clearly the flyover passes through the Class C and near the airport, but the disruption to IND is only brief. Then there's the aerial coverage, and that's overhead for the whole race. But the camera ship never goes far from the Speedway, and doesn't have to penetrate the Class C inner ring very much. Flight altitude may put the camera ship continuously in the Class C, though. How high do they fly? 1000 AGL? On race weekend I'll try to remember to look at what the TFR says.